Question

Tell whether the data in the table can be modeled by a linear equation. Explain.

Answer 1

Answer:

The table cannot be modeled by a linear equation.

Step-by-step explanation:

The data cannot be modeled by a linear equation because the rate of change is not constant.

If grab two set of points from the given data:

Let (x1, y1) = (1, 18)

(x2, y2) = (2, 15)

Plug these values into the slope formula:

$m = \frac{y2 - y1}{x2 - x1} = \frac{15 - 18}{2 - 1} = \frac{-3}{1} = -3$

Compare this slope with another set of ordered pairs:

(x1, y1) = (4, 12)

(x2, y2) = (8, 9)

$m = \frac{y2 - y1}{x2 - x1} = \frac{9 - 12}{8 - 4} = \frac{-3}{4}$

As you can see, the rate of change (slope) is not constant. Therefore, the given set of data cannot be modeled by a linear equation.

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